Ultrafast  Phenomena  in  Condensed  Ma3er  :  2    Prof.  P.Ruello  Ins:tut  des  Molécules  et  Matériaux  du  Mans,  UMR  6283  CNRS-­‐Université  du  Maine.

Ultrafast  Phenomena  in  Condensed  Ma3er  :  2   Prof.  P.Ruello    

Ins:tut  des  Molécules  et  Matériaux  du  Mans,  UMR   6283  CNRS-­‐Université  du  Maine.  

hν

pump probe

Acoustic phonons

1  

Ultra-­‐fast  phenomena  in  condensed  ma3er  physics        

-­‐5  Picosecond  acous:cs  :  Femtosecond  laser  genera:on  of  coherent  acous:c  phonon.  Electron-­‐

acous:c  phonon  coupling  :  thermoelas:city,  deforma:on  poten:al      

-­‐6  Evalua:on  of  elas:city  at  the  nanoscale  nanostructures  by  using  ultrashort  acous:c  pulses  :   echography  of  nanostructures  by  laser  optoacous:cs.  

OUTLINE  

2  

Ultra-­‐fast  phenomena  in  condensed  ma3er  physics        

-­‐5  Picosecond  acous:cs  :  Femtosecond  laser  genera:on  of  coherent  acous:c  phonon.  Electron-­‐

acous:c  phonon  coupling  :  thermoelas:city,  deforma:on  poten:al    

-­‐6  Evalua:on  of  elas:city  at  the  nanoscale  nanostructures  by  using  ultrashort  acous:c  pulses  :   echography  of  nanostructures  by  laser  optoacous:cs.  

OUTLINE  

3  

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4  

Genera:on  of  acous:c  waves  due  to  electronic  and   phononic  excita:on.    

!R

R = f (!!₁

!₁ ^,

!!₂

!₂ ⁾

! =!₁ +i!₂

GENERATION  :    

The  laser  excita:on  induces  varia:on  of   electronic  energy  and  the  relaxing  

electrons  emit  some  phonons  that  give   rise  to  an  increase  of  laTce  

temperature.  Consequently,  the  system   is  submi3ed  to  an  electronic  pressure   and  a  phononic  pressure.  Both  pressures   will  be  responsible  to  the  genera:on  of   a  front  of  acous:c  waves.  

!R R

pump  

5  

! = f (electrons, phonons)

Acous:c   phonons  

DETECTION  :    

6  

0e+00 1eï11 2eï11 3eï11 4eï11 5eï11 6eï11

0 500 1000 1500 2000 2500 3000 3500 4000 4500

Two  Temperatures  Model  

λ_e=10^6  (J.m^-­‐3.  K^-­‐1),  Ce=λ_eT_e     g=1e17  (W/m³.K)  

g=3e17  (W/m³.K)  

T_e    

T_L     Popula:on  of  phonons  =  laTce  

temperature  

Popula:on  of  excited  electron  =  hot   electrons  =  large  electronic  

temperature  T_e.  

Time(s)  

Temperature  (K)  

Phononic  stress  

(thermoelas:c  stress)   Electronic  stress  (deforma:on  

poten:al  stress)  

Deforma:on  poten:al  or  electronic  pressure  

We  have  shown  that  a  varia:on  of  the  volume  due  to  LA  mode  can  sca3er  electron  (change  of   the  electronic  level  of  the  electron)  by  deforma:on  poten:al  mechanism.  This  means  that   phonon  can  modify  the  distribu:on  of  electron  in  the  electronic  bands.  

In  the  inverse  a  change  of  the  electronic  energy  (by  laser  ac:on)  can  also  (reciprocally)  induce  a   change  of  the  laTce  volume  by  deforma:on  poten:al  mechanism.  The  photoexcited  electrons   have  new  “place”  within  the  crystal  than  they  had  before  laser  excita:on.  This  consequently   modify  the  local  electrosta:c  interac:on  that  forces  ca:ons  to  move.  Said  differently,  the  laser-­‐

induced  modifica:on  of  the  distribu:on  of  the  electron  in  the  bands  modify  indeed  the  orbitals   overlapping.  Consequently  the  equilibrium  posi:on  of  the  laTce  can  changes  (increase  or  

decrease  of  laTce  parameter  depending  on  the  electronic  structure).  

u! = !

u₀e^{i(q.! r!!wt)}

! = !u

!r = iq.u_Oe^{i(q.! r!"wt)}!

u_r = iq.! u

!H_e"LA = a_n,k.! = a_n,k.iq.u

An  acous:c  field  modifies  the   electronic  energy    

A  modifica:on  of  the  electronic  energy  

modifies  the  acous:c  field  (crea:on  of  phonon).    

!H_e"LA = a_n,k.! = a_n,k.iq.u

7  

Electron-­‐longitudinal  acous:c  phonon  coupling  

C   m   -­‐-­‐-­‐  

-­‐-­‐-­‐  

x   BV   BC  

E_g     E_g  +δU  

!^U = a!^V V

Sca3ering  of  the  electron  by  a   local  fluctua:on  of  the  electronic   band  structure  

Compression  (for  example)  

a=  deforma:on  poten:al  parameter  

δV/V  =  volume  varia:on  due  to  the  acous:c  phonon  

(macroscopic  laTce  distorsion)   ⁸  

Electronic  pressure  in  metals  (deforma:on  poten:al)  

P = 2 3

E V E = !²k²

2m g("

k)d

0 k_F

!

2k²

2m k² dk

!

!!

2k_F⁵ 10m!²

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"V

#

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'(

N

N = 4

3!^k_F³ ! V

8!^{3 !2}

Number  of  electrons  in   the  Fermi  sphere  

E(N,V) =

V!² !(N3!² V )^5/3

10m! ² The  internal  pressure  of  quantum  

free  electrons  depends  on  its   energy  E      

9  

(T=0K)  

P = 2 3

E

V !P " 2

3

!E

V " !_e^C_e^!T_e !_e = !"_e^C_e"T_e

When  a  laser  excite  an  electronic  cloud  in  a   metal  where  we  can  describe  the  electron   as  a  Fermi  liquid,  the  modifica:on  of  the   electronic  energy  induces  a  change  of  the   internal  pressure  

! Conven:on   External   applied     stress  

Compression  ! > 0

! < 0 Expansion  

C_e!T_e = !E /V

( )

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!P " N #1eV

V "10²⁸ #10^$19 =1GPa

Grüneisen  coeff   of  electrons  

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The  electronic  subsystem  relax  step  by  step  to  its  ini:al  state  by  emiTng  phonons.  This  increase  of  phonons   popula:on  increase  the  vibronic  energy  of  the  laTce  (increase  of  the  temperature  T_L).  Since  the  laTce  is   intrinsically  anharmonic,  the  laTce  expands.  This  is  called  the  phononic  pressure  or  thermoelas:c  stress.  

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!_therm = !3B"^"T

! _def.pot = !d_ehN = !NB "E_g

"P

= !3B! ^{N "(h}" ! E_g) C

Thermoelas:city  and  deforma:on  poten:al  in  GaAs  

16  

hv    

In  GaAs  :    

!

>> !

è  It  is  possible  to  generate  GHz-­‐THz    acous:c  phonons  in  GaAs   without  hea:ng  the  crystal  

Photoinduced  stress  

N : photocarriers concentration,

d_eh : deformation potential parameter B : bulk modulus,

β : thermal expansion coefficient, ΔT : lattice temperature

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Spectrum  of  the  emi3ed  acous:c   phonons  

19  

material

Pump beam (200fs)

Generation  of  acoustic  waves  by  a  femtosecond  laser

L

L=light  penetration  length  

=  characteristic  acoustic  wavelength In  metals  L  ~20nm

In  semiconductors  L  depends  a  lot   on  the  pump  wavelength.

Acoustic   pulse

 duration ! ! 2L V_S

V_s=5000m/s

! ! 6ps ^(166GHz)

Review  on  the  processes    :    

Laser  Optocacous4cs  ,  Karabutov,  Gusev,  AIP-­‐Press,    New  York,  1993  

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